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• Numerical modeling of thermoacoustic devices can be classified into 1-D linear and 2-D/3-D non-linear models. • Linear thermoacoustic models lose their utility, in the high amplitude and high frequency regime. • CFD modeling has proven to be an effective tool in capturing the nonlinearities associated with standing wave thermoacoustic devices. • Flow dominance in a 2-D plane inside SWTADs has allowed the performance evaluation of these devices utilizing 2-D CFD models. • CFD modeling of standing wave thermoacoustic devices primarily focus on stack and the region around it. Global environmental concerns have brought the challenge of developing renewable energy technologies to cope up with the world energy needs. Thermoacoustic devices present themselves as a viable alternative to replace conventional refrigeration and power systems due to their minimal carbon footprint. These devices involve complex flow physics encompassing transient phenomenon and conversion of acoustic and thermal energies for their efficient performance. With the rapid advancement in computational capabilities, extensive numerical work is carried out to gain detailed understanding of the thermoacoustic devices. In this paper, a detailed review of the numerical modeling techniques that have been applied in the field of Standing Wave Thermoacoustic Devices (SWTAD) is carried out. At first, a brief review of analytical method is presented and the need for numerical modeling is highlighted. Numerical modeling techniques ranging from simplified linear to detailed Computational Fluid Dynamics (CFD) models are reviewed in detail. Model configurations, capabilities and tools developed and utilized so far in the research area are summarized. Challenges associated with SWTAD and applications modeled using CFD are discussed. The paper concludes with some useful recommendations regarding the numerical modeling of thermoacoustic devices. [ABSTRACT FROM AUTHOR]